Question

A wire of uniform thickness with a resistance of $27\Omega$ is cut into three equal pieces and they are joined in parallel. The equivalent resistance of the parallel combination will be :

• A. $3\Omega$
• B. $9\Omega$
• C. $27\Omega$
• D. $49\Omega$

Answer 1

The correct option is A $3\Omega$

In this case, a wire of uniform thickness with a resistance of 27 is cut into three equal pieces and they are joined in parallel. As we know that the resistance is directly proportional to the length of the wire, $R\propto L$, so when the wire is cut into 3, the resistance of the cut wire is reduced to one third of the total resistance. That is, the resistance of each cut wire becomes 27/3= 9 ohms.
Now, when these 3 wires are connected in a parallel connection, the total resistance is given as $\frac{1}{9}+\frac{1}{9}+\frac{1}{9}=\frac{1}{0.333}=3ohms$.
Hence, the total resistance is now 3 ohms only.